# The topological origin of anomalous transport: Persistence of {\beta} in the face of varying correlation length

## TL;DR

This paper reveals that the topological structure of flow fields in porous media, characterized by the parameter beta in CTRW models, remains invariant with increasing correlation length, indicating a topological origin of anomalous transport.

## Contribution

It demonstrates that the beta parameter in CTRW models is topologically determined and remains unchanged despite increased correlation length, challenging traditional heterogeneity-based explanations.

## Key findings

- Beta remains constant with increasing correlation length.
- Flow field morphology is insensitive to conductivity value changes.
- Topological features underpin anomalous transport behavior.

## Abstract

Traditional concepts for flow in porous media assume that the heterogeneous distribution of hydraulic conductivity is the source for the contaminant temporal and spatial heavy tail, a process known as anomalous or non-Fickian transport; this anomalous transport behavior can be captured by the $\beta$ parameter in the continues time random walk (CTRW) framework. This study shows that with the increase in spatial correlation length, between these heterogeneous distributions of hydraulic conductivities, the anomaly of the flow reduces, yet the $\beta$ value is unchanged, suggesting that there is a topological component to the flow field, captured by the $\beta$. This finding is verified by an analysis of the flow field, showing that the changes in the conductivity values have little effect on the flow field morphology, which points to the topological component in the flow.

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Source: https://tomesphere.com/paper/1906.07061